AskSia

Plus

solve those question A1 (a) A three-year discount bond has a YTM of 5\% and face...

May 13, 2024

solve those question

1 Solution

Present Value Calculation: The current price of a discount bond is the present value of its face value

Formula: The present value (PV) is calculated using the formula

PV = \frac{FV}{(1 + r)^n}

, where FV is the face value, r is the yield to maturity (YTM), and n is the number of years until maturity

Calculation: Substituting the given values into the formula, we get

PV = \frac{100}{(1 + 0.05)^3}

1 Answer

PV = \frac{100}{(1 + 0.05)^3} = \frac{100}{1.157625} \approx 86.38

Key Concept

Present Value of a Discount Bond

Explanation

The current price of a discount bond is found by discounting its face value by the yield to maturity over the bond's term to maturity.

2 Solution

Yield to Maturity (YTM) Calculation: YTM is the internal rate of return of the bond, considering all coupon payments and the face value

Formula: The YTM is found by solving the equation

P = \sum_{t=1}^{n} \frac{C}{(1 + YTM)^t} + \frac{FV}{(1 + YTM)^n}

, where P is the price, C is the annual coupon payment, FV is the face value, and n is the number of years to maturity

Coupon Payment: Given a coupon rate of 5%, the annual coupon payment is

C = \frac{5\% \times 100}{1} = 5

Calculation: Since the price equals the face value, the equation simplifies to

100 = \sum_{t=1}^{10} \frac{5}{(1 + YTM)^t} + \frac{100}{(1 + YTM)^{10}}

. This equation must be solved numerically for YTM

2 Answer

YTM ≈ 5%

Key Concept

Explanation

3 Solution

Expectations Hypothesis: The hypothesis states that the forward rates implied by current long-term interest rates are equal to expected future short-term interest rates

Price Increase and Short Rate: If the price of the bond increases by 10%, it implies that the expected short rates have fallen, as bond prices and interest rates are inversely related

Calculation: The new short rate can be inferred from the change in the bond price, but the exact rate requires additional information or assumptions about the magnitude of the change in expectations

3 Answer

The exact level of the short rate cannot be determined without additional information.

Key Concept

Explanation

4 Solution

Regression Interpretation: The regression equation attempts to predict changes in YTM based on the difference between current YTM and current short-term interest rate (i)

Coefficients and t-ratios: The coefficient of 0.25 is the constant term, and the coefficient of 0.2 represents the sensitivity of YTM changes to the term spread (YTM - i). The t-ratios indicate the statistical significance of the estimates

Expectations Hypothesis Support: If the coefficient of the term spread is significantly different from zero, it suggests that other factors besides the expectations hypothesis are influencing YTM changes

4 Answer

The regression does not strongly support the Expectations Hypothesis, as the term spread is a significant predictor of YTM changes.

Key Concept

Explanation

5 Solution

Reasons for Failure: The Expectations Hypothesis may fail empirical tests due to the presence of a risk premium, liquidity preference, or other market imperfections

5 Answer

The Expectations Hypothesis may not hold due to risk premiums, liquidity preferences, or market imperfections that are not accounted for in the hypothesis.

Key Concept

Explanation